1. Chem 388: Molecular Dynamics and Molecular Modeling Continuum Electrostatics And MM-PBSA

2. Chem 388: Molecular Dynamics and Molecular Modeling Topics Poisson Equation Poisson-Boltzmann Equation Finite Difference Method Born Model Generalized Born Hydrophobic effect Free Energy Component Analysis

3. Chem 388: Molecular Dynamics and Molecular Modeling Electrostatics in Molecular Biophysics Electrostatic interactions are very long-ranged Most of the common biological macromolecules are highly charged so we cannot simply ignore electrostatic interactions! The cytoplasm of cells contains a relatively high concentration of dissolved ions such as Na +, Ca 2+ and Cl -

4. Chem 388: Molecular Dynamics and Molecular Modeling Electrostatic Steering AChE and Fasciculin 2 bind with electrostatically- steered, diffusion- controlled kinetics.

5. Chem 388: Molecular Dynamics and Molecular Modeling Coulomb Equation Electrostatic Potential Electrostatic work required to bring a charge q’ to the point r q’ in the potential

6. Chem 388: Molecular Dynamics and Molecular Modeling Distance Dependent Dielectric Function Local Dielectric Environment of B-DNA in Solution: Results from a 14 ns Molecular Dynamics Trajectory M. A. Young, B. Jayaram, and D. L. Beveridge* * J. Phys. Chem. B, 102 (39), 7666 -7669, 1998

7. Chem 388: Molecular Dynamics and Molecular Modeling Dielectric Screening Physical Basis of Dielectric Screening : Polarization Dipoles & Polarization Induced – Electronic ~2 Permanent – Orientational ~80 Reaction Field

8. Chem 388: Molecular Dynamics and Molecular Modeling Molecule in Solution Solute: Low dielectric region with fixed partial charges  p ~2-4 Solvent: High dielectric region with unlocalized charges  p ~80 Presence of dielectric boundaries presents the effects of an induced surface charge

9. Chem 388: Molecular Dynamics and Molecular Modeling Poisson Equation where - differential operator If a dielectric medium screens the field Poisson Equation Relative permittivity Electrostatic potential Charge density

10. Chem 388: Molecular Dynamics and Molecular Modeling Effect of Dissolved Electrolytes Mobile ions are distributed according to the Boltzmann statistics. Mean local concentration (c(r))of ions relative to bulk concentration (c bulk ) Ion Distribution

11. Chem 388: Molecular Dynamics and Molecular Modeling Poisson-Boltzmann Equation Poisson Equation Charge Distribution Poisson-Boltzmann Equation

12. Chem 388: Molecular Dynamics and Molecular Modeling Linear Poisson-Boltzmann Equation For For a charge balanced system where

13. Chem 388: Molecular Dynamics and Molecular Modeling Finite Difference Approximation N=1 for linear equation for nonlinear

14. Chem 388: Molecular Dynamics and Molecular Modeling Features of Continuum Model Location and magnitude of charges Surface features of solute and solvent boundary Difference in dielectric across the boundary Ionic strength Weakness: Ignores molecular nature of solvent Finite size of ions Ion-ion correlation effects

15. Chem 388: Molecular Dynamics and Molecular Modeling Total Electrostatic Energy

16. Chem 388: Molecular Dynamics and Molecular Modeling Molecular Surface Potential

17. Chem 388: Molecular Dynamics and Molecular Modeling Applications of FDPB Methods Solvation energy pKa Shifts Binding energies Conformational analysis Effect of ionic strength on binding

18. Chem 388: Molecular Dynamics and Molecular Modeling Solvation Energy Solvation thermodynamics of amino acids S. B. Dixit, B. Jayaram et al. J. Chem. Soc., Faraday Trans., 1997, 93(6), 1105- 1113

19. Chem 388: Molecular Dynamics and Molecular Modeling Accessible Surface Area Image source: http://www.netsci.org/Science/Compchem/feature14.html

20. Chem 388: Molecular Dynamics and Molecular Modeling Born Model of Solvation Generalized Born Equation A modification of the generalized Born theory B. Jayaram, Y. Liu and D. L. Beveridge J. Chem. Phys., 109, 1465-1471.

21. Chem 388: Molecular Dynamics and Molecular Modeling pKa Calculation Study the effect of site- directed mutations on change in pK value Potential at site I due to the original group -1 or 1 for an acidic or basic group

22. Chem 388: Molecular Dynamics and Molecular Modeling Free Energy of Conformational Change

23. Chem 388: Molecular Dynamics and Molecular Modeling Free Energy of Binding Macroscopic Models of Aqueous Solutions Barry Honig, Kim Sharp and An-Suei Yang J. Phys. Chem. 1993,97, 1101-1109

24. Chem 388: Molecular Dynamics and Molecular Modeling Thermodynamics of Protein-DNA Binding Jayaram et al. (1999) J. Comp. Phys. 151, 333.